Analysis of sequential circuits Analysis of sequential circuits

Analysis of sequential circuits

Analysis of sequential circuits • The analysis of a sequential circuit consists of obtaining a table or a diagram for the time sequence of inputs, outputs, and internal states. • It is also possible to write Boolean expressions that describe the behavior of the sequential circuit. • A logic diagram is recognized as a clocked sequential circuit if it includes flip-flops with clock inputs. • The flip-flops may be of any type, and the logic diagram may or may not include combinational logic gates. Steps for analyzing sequential circuits 2

Analysis of sequential circuits Equations: The outputs of the flip-flops represent the present-state variables. The inputs of the flip-flops determine the next state that the circuit will enter. and B(t) Present-state: A(t) Next-state: : A(t+1) and B(t+1) Equations: • Output: 3

Analysis of sequential circuits Equations: We can omit the designation (t) after each variable for convenience. Present-state: A(t) and B(t) Next-state: : A(t+1) and B(t+1) Equations: Output: • Output: 4

Analysis of sequential circuits Equations: another presentation 5

Analysis of sequential circuits State Table The time sequence of inputs, outputs, and flip-flop states can be enumerated in a state table (sometimes called a transition table). 6

Analysis of sequential circuits State Table • In general, a sequential circuit with m flip flops and n inputs needs 2 m+n rows in the state table. • The binary numbers from 0 through 2 m+n-1 are listed under the present-state and input columns. • The next-state section has m columns, one for each flip-flop. • The binary values for the next state are derived directly from the state equations. • The output section has as many columns as there are output variables. 7

Analysis of sequential circuits State Diagram (Finite State Machine (FSM)) • The information available in a state table can be represented graphically in the form of a state diagram. • A state is represented by a circle, and the (clock-triggered) transitions between states are indicated by directed lines connecting the circles. 8

Analysis of sequential circuits Example: D FF Equations: 9

Analysis of sequential circuits Example: JK FF Equations: 10

Analysis of sequential circuits 11

Analysis of sequential circuits 12

Analysis of sequential circuits 13

Analysis of sequential circuits Example: T FF Equations: 14

Analysis of sequential circuits Example: T FF 15

Analysis of sequential circuits Example: T FF 16